WASHINGTON — Slightly more fourth-graders nationwide are reading proficiently compared with a decade ago, but only a third of them are now reading well, according to a new report. The study also found the reading skills gap between children from lower-income and higher-income families has grown, and proficiency varies across states. Students in all but six states have improved reading proficiency, according to the report by the Annie E. Casey Foundation, which used reading scores from the National Assessment of Educational Progress, also known as the Nation’s Report Card, to compare reading skills of fourth-graders in 2013 and 2003. Maryland, the District of Columbia and Rhode Island saw the biggest gains, while reading levels declined in Alaska, Michigan, South Dakota and West Virginia. Reading proficiency remained level in Connecticut, which had the highest percentage of fourth-graders reading proficiently in 2003, and in Montana. Still, the range of reading skills across the states was striking. The proportion of fourth-grade students reading proficiently last year ranged from 21 percent in New Mexico and Mississippi to 57 percent in Massachusetts. Children from lower-income families fared worse on reading than those from higher-income families in every state, but the gap was largest in the District of Columbia, Massachusetts and Connecticut.